1. Field of the Invention
The present invention relates to nuclear magnetic resonance (NMR), and in particular, to Fourier encoding an NMR signal.
2. Description of the Related Technology
Pulsed-field gradient nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) tomography rely on Fourier encoding, a method by which the phase of the transverse magnetization is modulated by the application of a gradient in the component of the static field along some direction. The Fourier encoding performed prior to detecting NMR signals introduces spatially dependent phase differences in the NMR signals. To reconstruct the morphology of an object, multiple encodings are collected, and inverse Fourier transformation of the data set provides a map of the local spin density.
At high fields, where a ratio, ΔBmax/B0, of the maximum amplitude ΔBmax of the magnetic gradient field over the field of view or sample volume to the strength B0 of the static magnetic field is much less than 1, the resulting map of spin density is accurate because the spin Hamiltonian, which also contains perpendicular “concomitant” components, is truncated by the strong Zeeman interaction. (Truncation of the Hamiltonian is the averaging of rapidly oscillating concomitant components of the gradient field and is formally equivalent to first-order perturbation theory.) Thus, even though a pure gradient can never be created by Maxwell's equations, truncation makes unidirectional gradients possible in the rotating frame.
At low fields, this picture no longer provides an accurate description of the spin dynamics. As the ratio ΔBmax/B0 is increased, the concomitant fields cause severe distortions in the Fourier encoding and slice selection. When ΔBmax/B0 is 1, for example, planes of isofrequency are bent into spheres whose radius equals one half the field of view. Such distortions in the Fourier encoding can render Fourier encoding impractical in low-field NMR and imaging systems where ΔBmax approaches or even exceeds B0.